gh-36281: remove unused vars in matrix/
    
remove unused variables in matrix folder, as suggested by cython-lint

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36281
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert, Matthias Köppe

Author: Release Manager

src/sage/matrix/matrix0.pyx

@@ -524,7 +524,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         This is fast since it is a cdef function and there is no bounds
         checking.
         """
-        raise NotImplementedError("this must be defined in the derived class (type=%s)"%type(self))
+        raise NotImplementedError("this must be defined in the derived class (type=%s)" % type(self))
 
     cdef get_unsafe(self, Py_ssize_t i, Py_ssize_t j):
         """
@@ -1396,7 +1396,6 @@ cdef class Matrix(sage.structure.element.Matrix):
         """
         cdef list row_list
         cdef list col_list
-        cdef object index
         cdef Py_ssize_t row_list_len, col_list_len
         cdef list value_list
         cdef bint value_list_one_dimensional = 0
@@ -2241,7 +2240,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         tmp = [align*(b-a) for a,b in zip([0] + col_divs, col_divs + [nc])]
         format = '|'.join(tmp)
 
-        return "\\left" + matrix_delimiters[0] + "\\begin{array}{%s}\n"%format + s + "\n\\end{array}\\right" + matrix_delimiters[1]
+        return "\\left" + matrix_delimiters[0] + "\\begin{array}{%s}\n" % format + s + "\n\\end{array}\\right" + matrix_delimiters[1]
 
     ###################################################
     ## Basic Properties
@@ -2345,7 +2344,6 @@ cdef class Matrix(sage.structure.element.Matrix):
         if self._nrows != self._ncols:
             raise ArithmeticError("self must be a square matrix")
 
-        F = f.base_ring()
         vars = f.parent().gens()
         n = len(self.rows())
         ans = []
@@ -3746,7 +3744,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         """
         cdef dict d = {}
         cdef list queue = list(range(self._ncols))
-        cdef int l, sign, i, j
+        cdef int l, sign, i
 
         if skew:
             # testing the diagonal entries to be zero
@@ -4638,7 +4636,7 @@ cdef class Matrix(sage.structure.element.Matrix):
             print(self)
             print(self.nrows())
             print(self.dict())
-            raise RuntimeError("BUG: matrix pivots should have been set but weren't, matrix parent = '%s'"%self.parent())
+            raise RuntimeError("BUG: matrix pivots should have been set but weren't, matrix parent = '%s'" % self.parent())
         return tuple(x)
 
     def rank(self):

src/sage/matrix/matrix2.pyx

@@ -541,7 +541,7 @@ cdef class Matrix(Matrix1):
             ...
             ValueError: matrix equation has no solutions
 
-        A ValueError is raised if the input is invalid::
+        A :class:`ValueError` is raised if the input is invalid::
 
             sage: A = matrix(QQ,4,2, [0, -1, 1, 0, -2, 2, 1, 0])
             sage: B = matrix(QQ,2,2, [1, 0, 1, -1])
@@ -2184,7 +2184,7 @@ cdef class Matrix(Matrix1):
         Compute the determinant of the upper-left level x level submatrix
         of self. Does not handle degenerate cases, level MUST be >= 2
         """
-        cdef Py_ssize_t n, i
+        cdef Py_ssize_t i
         if level == 2:
             return self.get_unsafe(0,0) * self.get_unsafe(1,1) - self.get_unsafe(0,1) * self.get_unsafe(1,0)
         else:
@@ -3316,8 +3316,7 @@ cdef class Matrix(Matrix1):
             3
         """
         if self.nrows() == 0 or self.ncols() == 0:
-            return ZZ(1)
-        R = self.base_ring()
+            return ZZ.one()
         x = self.list()
         try:
             d = x[0].denominator()
@@ -3905,7 +3904,7 @@ cdef class Matrix(Matrix1):
         """
         tm = verbose("computing right kernel matrix over a domain for %sx%s matrix"
                      % (self.nrows(), self.ncols()), level=1)
-        d, u, v = self.smith_form()
+        d, _, v = self.smith_form()
         basis = []
         cdef Py_ssize_t i, nrows = self._nrows
         for i in range(self._ncols):
@@ -6098,7 +6097,7 @@ cdef class Matrix(Matrix1):
         # subrings of fields of which an algebraic closure is implemented.
         if format is None:
             try:
-                F = self.base_ring().fraction_field().algebraic_closure()
+                self.base_ring().fraction_field().algebraic_closure()
                 return 'all'
             except (NotImplementedError, AttributeError):
                 return 'galois'
@@ -6922,7 +6921,6 @@ cdef class Matrix(Matrix1):
             from warnings import warn
             warn("Using generic algorithm for an inexact ring, which may result in garbage from numerical precision issues.")
 
-        V = []
         from sage.categories.homset import hom
         eigenspaces = self.eigenspaces_left(format='galois', algebraic_multiplicity=True)
         evec_list=[]
@@ -8068,7 +8066,7 @@ cdef class Matrix(Matrix1):
         if self.fetch('in_echelon_form'):
             return self.fetch('pivots')
 
-        tm = verbose('generic in-place Gauss elimination on %s x %s matrix using %s algorithm'%(self._nrows, self._ncols, algorithm))
+        _ = verbose('generic in-place Gauss elimination on %s x %s matrix using %s algorithm' % (self._nrows, self._ncols, algorithm))
         self.check_mutability()
         cdef Matrix A
 
@@ -8367,7 +8365,6 @@ cdef class Matrix(Matrix1):
         """
         if subdivide not in [True, False]:
             raise TypeError("subdivide must be True or False, not %s" % subdivide)
-        R = self.base_ring()
         ident = self.matrix_space(self.nrows(), self.nrows()).one()
         E = self.augment(ident)
         extended = E.echelon_form(**kwds)
@@ -12227,7 +12224,7 @@ cdef class Matrix(Matrix1):
         Returns a pair (F, C) such that the rows of C form a symplectic
         basis for self and F = C \* self \* C.transpose().
 
-        Raises a ValueError if not over a field, or self is not
+        Raises a :class:`ValueError` if not over a field, or self is not
         anti-symmetric, or self is not alternating.
 
         Anti-symmetric means that `M = -M^t`. Alternating means
@@ -15396,7 +15393,7 @@ cdef class Matrix(Matrix1):
         if p == 2:
             A = self.change_ring(CDF)
             A = A.conjugate().transpose() * A
-            U, S, V = A.SVD()
+            S = A.SVD()[1]
             return max(S.list()).real().sqrt()
 
         A = self.apply_map(abs, R=RDF)
@@ -15887,7 +15884,6 @@ cdef class Matrix(Matrix1):
             dd, uu, vv = mm.smith_form(transformation=True)
         else:
             dd = mm.smith_form(transformation=False)
-        mone = self.new_matrix(1, 1, [1])
         d = dd.new_matrix(1,1,[t[0,0]]).block_sum(dd)
         if transformation:
             u = uu.new_matrix(1,1,[1]).block_sum(uu) * u
@@ -16081,18 +16077,17 @@ cdef class Matrix(Matrix1):
             sage: U * A == H
             True
         """
-        left, H, pivots = self._echelon_form_PID()
+        left, H, _ = self._echelon_form_PID()
         if not include_zero_rows:
             i = H.nrows() - 1
             while H.row(i) == 0:
                 i -= 1
-            H = H[:i+1]
+            H = H[:i + 1]
             if transformation:
-                left = left[:i+1]
+                left = left[:i + 1]
         if transformation:
             return H, left
-        else:
-            return H
+        return H
 
     def _echelon_form_PID(self):
         r"""

src/sage/matrix/matrix_cyclo_dense.pyx

@@ -40,7 +40,7 @@ AUTHORS:
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #*****************************************************************************
 
 from cysignals.signals cimport sig_on, sig_off
@@ -51,7 +51,7 @@ from sage.structure.element cimport Element
 from sage.misc.randstate cimport randstate, current_randstate
 from sage.libs.gmp.randomize cimport *
 
-from sage.libs.flint.types cimport fmpz_t, fmpq
+from sage.libs.flint.types cimport fmpz_t
 from sage.libs.flint.fmpz cimport fmpz_init, fmpz_clear, fmpz_set_mpz, fmpz_one, fmpz_get_mpz, fmpz_add, fmpz_mul, fmpz_sub, fmpz_mul_si, fmpz_mul_si, fmpz_mul_si, fmpz_divexact, fmpz_lcm
 from sage.libs.flint.fmpq cimport fmpq_is_zero, fmpq_set_mpq, fmpq_canonicalise
 from sage.libs.flint.fmpq_mat cimport fmpq_mat_entry_num, fmpq_mat_entry_den, fmpq_mat_entry
@@ -327,7 +327,7 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
         cdef Py_ssize_t k, c
         cdef NumberFieldElement x
         cdef NumberFieldElement_quadratic xq
-        cdef mpz_t quo, tmp
+        cdef mpz_t tmp
         cdef fmpz_t denom, ftmp
         cdef ZZ_c coeff
 
@@ -1036,7 +1036,6 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
         """
         cdef Py_ssize_t i
         cdef Matrix_rational_dense mat = self._matrix
-        cdef fmpq * entry
         cdef mpq_t tmp
 
         sig_on()
@@ -1198,8 +1197,6 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
         if self._nrows <= 3:
             return max(1, 3*B, 6*B**2, 4*B**3)
 
-        # This is an approximation to 2^(5/6*log_2(5) - 2/3*log_2(6))
-        alpha = RealNumber('1.15799718800731')
         # This is 2*e^(1-(2(7\gamma-4))/(13(3-2\gamma))), where \gamma
         # is Euler's constant.
         delta = RealNumber('5.418236')
@@ -1333,20 +1330,20 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
             [4 0 0]
             [0 0 0]
         """
-        tm = verbose("Computing characteristic polynomial of cyclotomic matrix modulo %s."%p)
+        tm = verbose("Computing characteristic polynomial of cyclotomic matrix modulo %s." % p)
         # Reduce self modulo all primes over p
-        R, denom = self._reductions(p)
+        R, _ = self._reductions(p)
         # Compute the characteristic polynomial of each reduced matrix
         F = [A.charpoly('x') for A in R]
         # Put the characteristic polynomials together as the rows of a mod-p matrix
         k = R[0].base_ring()
-        S = matrix(k, len(F), self.nrows()+1, [f.list() for f in F])
+        S = matrix(k, len(F), self.nrows() + 1, [f.list() for f in F])
         # multiply by inverse of reduction matrix to lift
         _, L = self._reduction_matrix(p)
         X = L * S
         # Now the columns of the matrix X define the entries of the
         # charpoly modulo p.
-        verbose("Finished computing charpoly mod %s."%p, tm)
+        verbose("Finished computing charpoly mod %s." % p, tm)
         return X
 
     def _charpoly_multimodular(self, var='x', proof=None):
@@ -1676,7 +1673,6 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
             [   1    0 7/19]
             [   0    1 3/19]
         """
-        cdef int i
         cdef Matrix_cyclo_dense res
         cdef bint is_square
 
@@ -1827,14 +1823,11 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
             Traceback (most recent call last):
             ...
             ValueError: echelon form mod 7 not defined
-
         """
-        cdef Matrix_cyclo_dense res
         cdef int i
 
         # Initialize variables
-        is_square = self._nrows == self._ncols
-        ls, denom = self._reductions(p)
+        ls, _ = self._reductions(p)
 
         # Find our first echelon form, and the associated list
         # of pivots
@@ -1936,13 +1929,11 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
         X = R._generator_matrix()
         d = self._degree
         MS = MatrixSpace(QQ, d, d)
-        mlst = self.list()
         for c in self._matrix.columns():
             v = c.list()
             for n in range(d-1):
                 c = c * X
                 v += c.list()
-            temp = MS(v)
             rmul = MS([v[d*i+j] for j in range(d) for i in range(d)]) # We take the transpose
             l.append(rmul * A._rational_matrix())
 

src/sage/matrix/matrix_integer_dense.pyx

@@ -520,7 +520,6 @@ cdef class Matrix_integer_dense(Matrix_dense):
         # TODO: *maybe* redo this to use mpz_import and mpz_export
         # from sec 5.14 of the GMP manual. ??
         cdef int i, j, len_so_far, m, n
-        cdef char *a
         cdef char *s
         cdef char *t
         cdef char *tmp
@@ -1537,17 +1536,13 @@ cdef class Matrix_integer_dense(Matrix_dense):
         """
         cdef Integer h
         cdef Matrix_integer_dense left = <Matrix_integer_dense>self
-        cdef mod_int *moduli
-        cdef int i, n, k
+        cdef int i, k
 
         nr = left._nrows
         nc = right._ncols
-        snc = left._ncols
-
 
         cdef Matrix_integer_dense result
 
-
         h = left.height() * right.height() * left.ncols()
         verbose('multiplying matrices of height %s and %s'%(left.height(),right.height()))
         mm = MultiModularBasis(h)
@@ -1601,7 +1596,6 @@ cdef class Matrix_integer_dense(Matrix_dense):
         from .matrix_modn_dense_double import MAX_MODULUS as MAX_MODULUS_DOUBLE
 
         cdef Py_ssize_t i, j
-        cdef mpz_t* self_row
 
         cdef float* res_row_f
         cdef Matrix_modn_dense_float res_f
@@ -2015,7 +2009,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
         if ans is not None:
             return ans
 
-        cdef Matrix_integer_dense H_m,w,U
+        cdef Matrix_integer_dense H_m, U
         cdef Py_ssize_t nr, nc, n, i, j
         nr = self._nrows
         nc = self._ncols
@@ -3757,7 +3751,6 @@ cdef class Matrix_integer_dense(Matrix_dense):
         if not self.is_square():
             raise ValueError("self must be a square matrix")
 
-        cdef Py_ssize_t n = self.nrows()
         cdef Integer det = Integer()
         cdef fmpz_t e
 
@@ -4884,7 +4877,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
             [  0   0 545], [0, 1, 2]
             )
         """
-        cdef Py_ssize_t i, j, piv, n = self._nrows, m = self._ncols
+        cdef Py_ssize_t i, j, n = self._nrows, m = self._ncols
 
         from .constructor import matrix
 
@@ -5380,9 +5373,8 @@ cdef class Matrix_integer_dense(Matrix_dense):
         n = ns + na
 
         cdef Matrix_integer_dense Z
-        Z = self.new_matrix(nrows = m, ncols = n)
-        cdef Py_ssize_t i, j, p, qs, qa
-        p, qs, qa = 0, 0, 0
+        Z = self.new_matrix(nrows=m, ncols=n)
+        cdef Py_ssize_t i, j
         for i from 0 <= i < m:
             for j from 0 <= j < ns:
                 fmpz_set(fmpz_mat_entry(Z._matrix,i,j),
@@ -5455,7 +5447,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
         Return matrix obtained from self by deleting all zero columns along
         with the positions of those columns.
 
-        OUTPUT: matrix list of integers
+        OUTPUT: (matrix, list of integers)
 
         EXAMPLES::
 
@@ -5468,10 +5460,9 @@ cdef class Matrix_integer_dense(Matrix_dense):
             [-1  5], [1]
             )
         """
-        C = self.columns()
-        zero_cols = [i for i,v in enumerate(self.columns()) if v.is_zero()]
+        zero_cols = [i for i, v in enumerate(self.columns()) if v.is_zero()]
         s = set(zero_cols)
-        nonzero_cols = [i for i in range(self.ncols()) if not (i in s)]
+        nonzero_cols = [i for i in range(self.ncols()) if i not in s]
         return self.matrix_from_columns(nonzero_cols), zero_cols
 
     def _insert_zero_columns(self, cols):